The goal of this project was to understand the role of tetrahydrofuran (THF) in promoting the enclathration of methane. A molecular-scale understanding of this process requires understanding how additives change the solubility of the solute of interest (here methane). In this concluding report, I summarize key achievements, challenges we faced, and future directions.

Regularizing binding energy distributions to calculate free energies — a new framework to model solvation phenomena: We developed a new approach to calculate the hydration free energy, one that sidesteps the current dominant paradigm based on alchemically changing solutes. Our approach leads to a transparent accounting of the hydration thermodynamics in terms of contributions from (a) local, chemically specific solute-solvent interactions, (b) long-range, nonspecific solute-solvent interactions, and (c) solution properties independent of the solute. The framework is readily applicable to systems modeled by ab initio potentials or molecularly complex solutes such as THF, neopentane, or macromolecules.

The high-energy tail of the distribution of solute-solvent interaction energies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the short-range repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess chemical potential of the solute.

We have applied this technique to study the hydration free energy of water using both classical and ab initio simulations, and of hydrate promoters such as ethylene oxide (ETO), trimethylene oxide, and THF.

Challenges: Our studies on hydrate promoters reveal deficiencies in the forcefield for these molecules. For example, the hydration free energy of THF is somewhat more positive than the experimental value of about -2.5 kcal/mole. This likely explains why we barely see any changes in the solubility of methane in a 4.4 M solution of THF (data not shown). The presence of THF in pure water does increase the probability of forming voids in the medium (data not shown), suggesting solubility of methane should be enhanced in a THF-water mixture, as is also observed experimentally.

Coordination structure of water: In hydrates, water adopts ice-like arrangement; this phenomena has been invoked to explain the poor solubility with increasing temperature of hydrophobic molecules (such as methane) in water. The existence of fleeting ice-like arrangements in pure liquid water has itself been invoked to explain some of the unusual properties of water. Further, a controversial experimental study posits that in liquid water, water molecules are primarily coordinated to two other molecules forming chains of such hydrogen bonds. Using a theory that follows from the regularization approach, we found that in a well-studied classical model of water the free energy to form four water and one water clusters are nearly the same (J Chem Phys, 134, 124514, 2011). Thus in the observed tetra-coordinate structure of the solute water, only one water molecule can be considered chemically bonded to the solute water. Our study suggests that care be exercised in inferring chemical bonding between solute and solvent in a liquid, where intrinsic fluctuations of the solvent itself lead to transient changes in the coordination number of the solute.

Hydration of a macromolecule: We used the regularization framework to tackle a challenging problem of modeling the hydration of a macromolecule, here a protein. In a first-of-its-kind calculation, using the regularization framework we have calculated, within an all-atom approach, the hydration free energy of cytochrome C in both its discharged and fully charged states. This work also revealed the limitations of continuum solvent models. At the scale of the protein, the atomically detailed estimate of the nonpolar contribution was nearly twice that predicted by γ · SA, where SA is the solvent accessible surface area and γ is a surface energy based on standard literature values (obtained by parameterizing against solubility of small molecules). Further, the solvent electrostatic response to the protein is not linear; not surprisingly, a dielectric model was also found to have limitations. This work has been published in J. Chemical Theory and Computation, 8, 3409, 2012.

Student training: The ACS-PRF grant helped partially support the training of one graduate student, who has since graduated and joined Intel (Portland). It also helped partially support another graduate student in summer 2012.

Publications: The grant resulted in eight (8) peer-reviewed publications. Two (2) of the papers J. Chem. Phys. 133, 141101, 2010 and J. Chem. Phys. 135, 181101, 2011 which were among top monthly downloaded articles in the months of October 2010 and November 2011, respectively. One additional publication is in preparation.